Contents All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laboratories as a new resource as real as energy.

demonstrate the relevance of entanglement, Bell inequalities and decoherence in particle physics. In particular, we study in detail the features of the “strange ” K 0 ¯ K 0 system as an example of entangled meson–antimeson systems. The analogies and differences to entangled spin – 1 2 or photon systems are worked, the effects of a unitary time evolution of the meson system is demonstrated explicitly. After an introduction we present several types of Bell inequalities and show a remarkable connection to CP violation. We investigate the stability of entangled quantum systems pursuing the question how possible decoherence might arise due to the interaction of the system with its “environment”. The decoherence is strikingly connected to the entanglement loss of common entanglement measures. Finally, some outlook of the field is presented. 1

We construct a set of PPT (positive partial transpose) states and show that these PPT states are not separable, thus present a class of bound entangled quantum states.

Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagram can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Turing and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics.

Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum system, resulting in the coherent information and introduced here the compatible information measures, respectively. A sketch of an information optimization of a quantum experimental setup is proposed.

Entanglement or separability: the choice of how to factorize

The Gell-Mann λ matrices for Lie algebra su(3) are the natural basis for the Hilbert space of Hermitian operators acting on the states of a three-level system(qutrit). So the construction of EWs for two-qutrit states by using these matrices may be an interesting problem. In this paper, several two-qutrit EWs are constructed based on the Gell-Mann matrices by using the linear programming (LP) method exactly or approximately. The decomposability and non-decomposability of constructed EWs are also discussed and it is shown that the λ-diagonal EWs presented in this paper are all decomposable but by adding λ-non-diagonal terms, one can obtain various non-decomposable EWs.

Abstract We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in terms of the spectrum of the factor operators in the tensor summands.

In this paper based on the notion of entanglement witness, a new measure of entanglement called floating entanglement witness measure is introduced which satisfies some of the usual properties of a good entanglement measure. By exploiting genetic algorithm, we introduce a classical algorithm that computes floating entanglement witness measure. This algorithm also provides a method for finding entanglement witness for a given entangled state.

The Deutsch-Jozsa algorithm is a generalization of the Deutsch algorithm which was the first algorithm written. We present schemes to implement the Deutsch algorithm and the Deutsch-Jozsa algorithm via cavity QED. PACS: 03.65.Ud; 03.67.Mn; 32.80.-t; 42.50.-p Keywords: Deutsch algorithm; Deutsch-Jozsa algorithm; quantum computation; quantum algorithms; cavity QED. 1